Patients with previously treated multiple myeloma and kidney dysfunction will be treated with lenalidomide and low-dose dexamethasone. Phase I will study the side effects and best dose of lenalidomide when given together with low-dose dexamethasone therapy. After the maximum safe and tolerated dose is found in Phase I, the study will proceed to Phase II. Phase II will study how well the the treatment works in patients with previously treated (relapsed or refractory) multiple myeloma and kidney dysfunction. Biological therapies, such as lenalidomide, may stimulate the immune system in different ways and stop cancer cells from growing. Drugs used in chemotherapy, such as dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving lenalidomide together with dexamethasone may kill more cancer cells. Lenalidomide and dexamethasone may have different effects in patients who have changes in their kidney function.